High-dimensional data analysis with low-dimensional models : principles, computation, and applications

著者

    • Wright, John
    • Ma, Yi

書誌事項

High-dimensional data analysis with low-dimensional models : principles, computation, and applications

John Wright, Yi Ma

Cambridge University Press, 2022

  • : hardback

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注記

Includes bibliographical references (p. [633]-670) and index

内容説明・目次

内容説明

Connecting theory with practice, this systematic and rigorous introduction covers the fundamental principles, algorithms and applications of key mathematical models for high-dimensional data analysis. Comprehensive in its approach, it provides unified coverage of many different low-dimensional models and analytical techniques, including sparse and low-rank models, and both convex and non-convex formulations. Readers will learn how to develop efficient and scalable algorithms for solving real-world problems, supported by numerous examples and exercises throughout, and how to use the computational tools learnt in several application contexts. Applications presented include scientific imaging, communication, face recognition, 3D vision, and deep networks for classification. With code available online, this is an ideal textbook for senior and graduate students in computer science, data science, and electrical engineering, as well as for those taking courses on sparsity, low-dimensional structures, and high-dimensional data. Foreword by Emmanuel Candes.

目次

  • Foreword
  • Preface
  • Acknowledgements
  • 1. Introduction
  • Part I. Principles of Low-Dimensional Models: 2. Sparse Signal Models
  • 3. Convex Methods for Sparse Signal Recovery
  • 4. Convex Methods for Low-Rank Matrix Recovery
  • 5. Decomposing Low-Rank and Sparse Matrices
  • 6. Recovering General Low-Dimensional Models
  • 7. Nonconvex Methods for Low-Dimensional Models
  • Part II. Computation for Large-Scale Problems: 8. Convex Optimization for Structured Signal Recovery
  • 9. Nonconvex Optimization for High-Dimensional Problems
  • Part III. Applications to Real-World Problems: 10. Magnetic Resonance Imaging
  • 11. Wideband Spectrum Sensing
  • 12. Scientific Imaging Problems
  • 13. Robust Face Recognition
  • 14. Robust Photometric Stereo
  • 15. Structured Texture Recovery
  • 16. Deep Networks for Classification
  • Appendices: Appendix A. Facts from Linear Algebra and Matrix Analysis
  • Appendix B. Convex Sets and Functions
  • Appendix C. Optimization Problems and Optimality Conditions
  • Appendix D. Methods for Optimization
  • Appendix E. Facts from High-Dimensional Statistics
  • Bibliography
  • List of Symbols
  • Index.

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